Choosing the Right Graph

A column graph is the picture version of a frequency table, and it is the display to reach for when your data is categorical. Each group gets its own column, and the height of the column is the frequency. Here twenty students chose their favourite fruit, and one glance tells you apple wins with seven and grapes comes last with three. Three rules keep it correct. Leave gaps between the columns, because the groups are separate things and not points on a number line. Make every column the same width, so no group looks more important than it is. And start the frequency scale at nought. You can turn the whole thing sideways into bars if you prefer, and the rules stay the same.

A dot plot suits small sets of counted numerical data. You draw a number line, then stack one dot above the line for every value in your data. Here are the fifteen sibling answers again, and the shape is instantly clear: the tallest stack sits above one, so one sibling is the most common answer. Because there is a dot for every student, nothing is hidden — count all the dots and you get fifteen, and you can see the answers run from nought up to four. The limitation is size. Two hundred values would need two hundred dots and the plot would become unreadable, so keep dot plots for small sets. And stack the dots neatly in line, or the heights stop meaning anything.

A line graph is the one to use when the bottom axis is time. Plot a point for each day and join the points in order, and the line shows you the trend. Here the midday temperature climbs from twenty-two degrees on Monday to twenty-eight on Wednesday, then falls away to twenty-one by Friday. The steeper the line, the faster the change. What makes joining the points sensible is that time flows continuously: there really are moments between Monday and Tuesday, so the line stands for something. That is exactly why you must not join the columns on a fruit graph. There is nothing in between apple and banana, so a line there would be meaningless.

A picture graph, sometimes called a pictograph, uses a repeated symbol instead of a column. It looks friendly and it works well for small whole-number data, but there is one rule you cannot skip: it must have a key telling you what one symbol stands for. Here one book symbol stands for two books. So Wednesday shows five symbols, and five times two gives ten books, while Tuesday shows two symbols, meaning four books. To read any row, count the symbols and multiply by the number in the key. Without a key the picture is useless, because five symbols could just as easily mean five books, ten books or five hundred books, and nobody could tell which.

Here are all four side by side. A column graph is for categorical data and has gaps between its columns. A dot plot is for small sets of counted numerical data and shows one dot per value. A line graph is for change over time, with the points joined in order. And a picture graph uses repeated symbols with a key, which suits small whole-number data. Start by asking what kind of data you have, and the choice usually makes itself. Then, whichever you draw, four things are always required: a title, labels on both axes, an even scale starting at nought, and a key if you used symbols. Those four earn marks on their own, however neatly the data is plotted.